Read the phrase below.
the quotient of three less than a number and six more than four × a number
Which expression is equivalent to this phrase?

Rationale

(x-3)/(4x + 6)

The expression represents the quotient of three less than a number (x) and six more than four times that number. This correctly translates the mathematical phrase into an algebraic expression where the numerator is derived from subtracting 3 from x, and the denominator is formed by adding 6 to 4 times x.

A ((3-x)/(4x + 6)) YOUR ANSWER

This expression incorrectly represents the numerator. Instead of three less than a number, it presents three subtracted from x, which changes the intended meaning. The correct numerator should show x - 3, not 3 - x.

B ((x - 3)(4x + 6)) YOUR ANSWER

This choice represents a product rather than a quotient. The phrase specifies a quotient, indicating division between two expressions. Thus, this answer does not reflect the required operation and is therefore incorrect.

D (4x - 3 + 6) YOUR ANSWER

This expression simplifies to 4x + 3, which does not represent a quotient and fails to align with the original phrase. It combines the terms incorrectly and ignores the requirement of a division operation as specified in the question.

Conclusion

The correct expression that represents the phrase provided is (x-3)/(4x + 6), which accurately captures the quotient of three less than a number and six more than four times that number. The other choices, whether they misinterpret the operations involved or fail to represent the quotient, do not meet the requirements laid out in the question. Understanding how to translate words into mathematical expressions is crucial for solving algebraic problems accurately.

Read the phrase below. the quotient of three less than a number and six more than four × a number Which expression is equivalent to this phrase?

(x-3)/(4x + 6)

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Read the phrase below.
the quotient of three less than a number and six more than four × a number
Which expression is equivalent to this phrase?